Melt 1 tablespoon ghee in a large, heavy skillet over medium-low heat. Add the onions to the pan and sprinkle with the teaspoon salt. Cook, stirring frequently, until the onions are golden and caramelized, about 20 minutes; add the garlic and continue cooking for another 5 minutes – don’t allow the onions to burn. Using a slotted spoon, transfer the onion to a bowl and set aside.

While the onions are cooking, crumble the breakfast sausage into a small skillet and cook over medium-high heat until no longer pink, about 10 minutes. Remove from the heat and set aside.

Also while the onions are cooking, bring 2 quarts of salted water to a roiling boil. Carefully add the potatoes and cook for 5 minutes. Drain the potatoes and rinse with very cold water to cool.

Melt the remaining 2 tablespoons of ghee over medium-high heat in the skillet used to cook the onions. Cook the potatoes, stirring frequently, until they begin to turn golden brown, about 7 to 10 minutes; season with the salt, pepper and basil. Remove from the heat, and stir in the onions and sausage until well-mixed.

Make 6 wells in the hash; crack an egg in each well; bake for 15 minutes or until the whites are set but the yolks are not. Serve immediately.

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